Neuroblastoma remains a fatal disease fo a large percentage of patients, especially those wiht high risk features who become resistant to conventional therapy. This study is a limited institution pilot study designed to investigate the combination of buthionine sulfoximine (BSO) and melphalan (LPAM) in high risk neuroblastoma patients with progressive disease. The specific aims are: 1) to determine the toxicity of the combination of BSO and LPAM in pediatric patients with progressive neuroblastoma; 2) to determine the pharmacokinetics of hte combination of BSO and LPAM in pediatric patients; 3) to determine the ability of BSO to deplete gluthathione from tumor in marrow, normal marrow cells, and peripheral lymphocytes in pediatric patients; 4) to determine the response rate of neuroblastoma to BSO and LPAM within the confines of a pilot study.